Factor. I am not sure how to work this one out?

Question

3a^2(a – b) – 6a(a – b) + 21(a – b)
my answers are but no clue how to work it out.
A)(a – b)(3a2 – 6a + 21)
B)3(a – b)(a2 – 2a + 7)
C)3(a – b)(a2 – 6a + 21)
D)(3a – b)(a2 – 2a + 7)

Answer 1

Hi,

Divide each term by 3(a - b) as the GCF.

3a²(a–b)...6a(a–b)...21(a–b)
------------.-.------------+----------
..3(a - b)....3(a - b)......3(a-b)

3(a-b)(a² - 2a + 7) <== Answer B

Answer 2

Notice that all 3 terms that are being added and subtracted have "(a - b)" as a factor.
When you factor out (a - b), you have:
(a - b)(3a^2 - 6a + 21)
In the right parenthesis, you can factor out 3 from all 3 terms.
You now have:
3(a - b)(a^2 - 2a + 7)
which is answer B.
You could have did this in one step by noticing that you can factor out "3(a - b)".

Answer 3

Notice you face a-b for a factor to all 3, so you can factor that out as a group
(a-b)(3a^2-6a+21) or A

Answer 4

well
first off you would factor out what is in the parenthesis out of each factor,. so you take out the (a-b) from each. you get (a-b)multiplied by 3a^2 - 6a +21. then you factor out a 3 as well, and you get 3(a-b) times a^2 -2a + 7 u get B

Answer 5

The answer is B.

I believe the way of realizing this is by lots of practice.
First i'd facto the mos ovbious part: the term (a-b) is on all terms, so you factor the equation like this:

(a-b) ( 3a^2- 6a + 21)

If you distrubite the product go get the original formula you started with.

Now, you check the numbers.... another way of writing 6 and 21 is: 6x2 & 3x7 ...now you have something else you can factor, 3 is again on all terms:

(a-b)(3a^2 - 2x3 + 3x7)=(a-b).3.(a^2-2+7)

And that's option B.

Answer 6

3a^2(a - b) - 6a(a-b) + 21(a-b) =
(a-b)(3a^2 - 6a + 21) =
(a-b)3(a^2 - 2a +7) =
3(a-b)(a^2 - 2a +7)

Answer 7

(a - b) is can be factored out:

(a - b) (3a² - 6a + 21)

This equation cannot be factored anymore: (3a² - 6a +21)

So with that, your final answer should be:

(a - b) (3a² - 6a + 21)

option A and option B are both correct.

Answer 8

(a - b) (3a² - 6a + 21)
3 (a - b) (a² - 2a + 7)
ANSWER B

Answer 9

(3a^3-3a^2b)-(6a^2-6ab)+(21a-21b)....by multiplying.
3a^3-3a^2b-6a^2+6ab+21a-21b
3a^3-9a^2b+21a+21b....by gathering like terms..
I hate to simplify this kind of equation...sorry
but...A seems the right answer. for real